This texture synthesis algorithm is basically a 2D implementation of Synthesis of Bidirectional Texture Functions on Arbitrary Surfaces by Tong, Zhang, Liu, Wang and Guo. The algorithm still retains the underlying structure of the previous fast version, however in this version the multiresolution is implemented via a Gaussian pyramid of the input image (instead of a decimated quadtree as in the fast version). The neighbourhood search algorithm has also been modified. In this version a k nearest neighbour lookup table is used, as in Synthesis of Bidirectional Texture Functions on Arbitrary Surfaces by Tong, Zhang, Liu, Wang and Guo. There is one slight difference though in this implementation, when the k nearest neighbour lookup table is constructed, a smaller starting set is used from which the k nearest neighbours are found. This was done to save memory and computational time. Consult the code and their paper for more information.

This version of the Semi Causal Nonparametric Markov Random Field Texture Synthesis is not as fast as the fast version, but it does offer some advantages. For one, there does appear to be a reduction in the speckle noise that was apparent in the images synthesised by the fast version. Also, due to the nearest neighbour search algorithm, better blending is achieved between different phases of the synthetic texture. However, there is a loss in texture detail also due to the nearest neighbour search algorithm. One possible solution was presented by Hertzman etal. Image Analogies: A General Texture Transfer Framework, in which the two nearest neighbour search techniques were used. Depending on a closeness of fit criteria, the result was taken from either one or the other search techniques. However the closeness of fit criteria depended on a slightly arbitrary input parameter.

Source Code

The source code requires ImageMagick to be preinstalled. To compile the code, run gmake in the parent directory. There are two makefiles, one in parent directory, and in the src directory. If the code does not compile, both makefiles will need to be edited. I have written one for a sun (default) and one for an sgi machine, but I give no guarantees that they will work.

Synthesis run times for various input parameters

These times were compiled on a distributed system of mainly SunBlades 100: 500 MHz, 256 MBytes RAM. The input textures were 128x128 pixel images, and the output synthesised textures were 256x256 pixel images. The run times are basically dependent on output image size and the type of input texture. This is due to the nearest neighbour search algorithm used in the code. If the input texture is fairly uniform in colour, then the search algorithm will be more of an exhaustive search, and therefore more dependent on input image size. Time stamps are in "Days Hours:Minutes:Seconds".

Neighbourhood

# of Tests

Min Run Time

Max Run Time

Mean Run Time

Stdev Run Time

1

165

0 0:04:05

0 0:12:24

0 0:04:42

0 0:01:06

1 -c

165

0 0:04:05

0 0:12:21

0 0:04:38

0 0:01:09

1 -s

165

0 0:04:30

0 0:13:48

0 0:05:11

0 0:01:17

1 -s -c

165

0 0:04:33

0 0:14:19

0 0:05:11

0 0:01:24

2

165

0 0:05:18

0 0:16:28

0 0:06:17

0 0:01:25

2 -c

165

0 0:05:28

0 0:09:50

0 0:06:22

0 0:01:10

2 -s

165

0 0:11:00

0 0:21:10

0 0:13:17

0 0:02:05

2 -s -c

165

0 0:11:21

0 0:23:09

0 0:13:54

0 0:02:39

3

165

0 0:06:30

0 0:20:28

0 0:07:36

0 0:01:32

3 -c

165

0 0:06:36

0 0:21:23

0 0:08:03

0 0:02:08

3 -s

165

0 0:34:25

0 1:56:03

0 0:44:45

0 0:09:46

3 -s -c

165

0 0:36:11

0 1:56:12

0 0:46:51

0 0:09:41

4

165

0 0:07:30

0 0:15:11

0 0:08:52

0 0:01:33

4 -c

165

0 0:07:36

0 0:26:03

0 0:09:21

0 0:02:24

4 -s

165

0 1:34:30

0 5:37:25

0 2:08:30

0 0:32:01

4 -s -c

165

0 1:43:16

0 5:48:46

0 2:17:23

0 0:30:42

Additional Information

As in Greg Turk's algorithm Texture Synthesis on Surfaces, every pixel in the Gaussian pyramid is visited twice. However better results maybe obtained by either increasing the neighbourhood size or modifying the probability update function pUpdateFn() so that each pixel is visited more than twice (as in this version).

To compare this algorithm with other algorithms, it is necessary to use the same neighbourhood for each.